数据、模型与决策(运筹学)课后习题和案例答案011

CHAPTER 11

GOAL PROGRAMMING Review Questions

11.1-1 The management science team has been asked to analyze what the new product mix should

be for the three new products.

11.1-2 1. Achieve a total profit of at least $125 million.

2. Maintain the current employment level of 4,000 employees.

3. Keep capital investment down to no more than $55 million.

11.1-3 When using a goal programming approach, the total number of penalty points incurred by

missing goals is to be minimized.

11.2-1 Goal programming does not possess the characteristic of a single objective function.

11.2-2 The basic approach of goal programming is to establish a specific numeric goal for each of

the objectives and then to seek a solution that balances how close this solution comes to

each of these goals.

11.2-3 The objective function represents the weighted sum of deviations of the individual

objective functions from their respective goals.

11.2-4 The changing cells show the amounts over or under the respective goals.

11.2-5 A goal programming model can be formulated as a linear programming model.

11.3-1 Preemptive goal programming should be used when there are such major differences in the

importance of the goals that it is not feasible to assign meaningful weights to these goals to measure their relative importance.

11.3-2 Preemptive goal programming beings by focusing solely on meeting the most important

goal, then doing the same for the second goal, and so on.

11.3-3 The main difference is in the target cell. Rather than using the weighted sum of deciations,

preemptive goal programming begins by minimizing only the deviation from the most

important goal.

11.3-4 A constraint is added that the deviation achieved on the more important goals must

continue to be met while switching to minimizing the less important goals.

11.3-5 The solution fully achieved the top three goals.

Problems

11.1 The coefficient for L7 is three times as large as the coefficient for K7.

11.2 a) Goal 1: Market share for Product 1 0.5x1 + 0.2 x3≥ 15%

Goal 2: Market share for Product 2 0.3x2 + 0.2 x3≥ 10%

Overall objective is to minimize W = amount under Goal 1 + amount under Goal 2

b)

c) Both goals of market share cannot be met with an advertising budget of $55 million.

With this budget, spending $13.33 million on campaign 1 and $41.67 million on

campaign 3, market shares of 15% and 8.33% can be achieved. Additional advertising

budget will be necessary to achieve the desired market share.

11.3 a)

Measure of Performance = E4 + SUMPRODUCT(I12:J13, I5:J6)

b) Emax should produce 15 units of product 3. While this does increase the present level

of employment by 25, it does maximize profit over the life of the new products and it

does not decrease next year’s earnings from the current level.

11.4 a) No, we would not expect the optimal solution to change. Goal 1 is already met, so

increasing the weight on that goal would not change anything. We already exceed goal

2, so decreasing the penalty weight for goal 2 would only decrease our desire to avoid

exceeding this goal.

b)